Experimental characterization of four ionization chamber types in magnetic fields including intra-type variation

Background and purpose For dosimetry in magnetic resonance (MR) guided radiotherapy, assessing the magnetic field correction factors of air-vented ionization chambers is crucial. Novel MR-optimized chambers reduce MR-imaging artefacts, enhancing their quality assurance utility. This study aimed to characterize two new MR-optimized ionization chambers with sensitive volumes of 0.07 and 0.016 cm3 regarding magnetic field correction factors and intra-type variation and compare them to their conventional counterparts. Material and methods Five chambers of each type were evaluated in a water phantom, using a clinical linear accelerator and an electromagnet, as well as a 1.5 T MR-linac system. The magnetic field correction factor kB→,Q, addressing the change of response caused by a magnetic field, was assessed together with its intra-type variation. MR-optimized and conventional chambers were compared using a Mann-Whitney U-Test. Results Considering 1.5 T and a perpendicular chamber orientation, we observed significant differences in the magnetic field-induced change in chamber reading between the two 0.016 cm3 chamber versions (p = 0.03). For a 7 MV beam, MR-optimized chambers (0.016/0.07 cm3) showed kB→,Q values of 1.0426(66) and 1.0463(44), compared to 1.0319(53) and 1.0480(41) of their conventional counterparts. In anti-parallel orientation, kB→,Q was 1.0012(69) and 0.9863(49) for the MR-optimized chambers. The average intra-type variation of kB→,Q over all chamber types was 0.3%. Conclusion Magnetic field correction factors were successfully determined for four ionization chamber types, including two new MR-optimized versions, allowing their use in MR-linac absolute dosimetry. Evaluation of the intra-type variation enabled the assessment of their contribution to the uncertainty of tabulated kB→,Q.


Introduction
The combination of real-time magnetic resonance (MR) imaging and a linear accelerator (linac) promises to improve the quality of treatment in radiation oncology [1].Hybrid devices, so-called MR-linacs, allow for online adaptive radiotherapy in which a treatment plan is adjusted to account for daily changes in a patient's anatomy as revealed by oncouch MR images [2].Using continuous MR-imaging, gating and tracking of moving targets seems feasible in MR-guided radiotherapy [3].
With the increasing use of MR-linac systems in clinical routine, robust, fast and accurate dosimetry protocols are required for quality assurance.Recent studies have characterized air-vented ionization chambers regarding their behaviour in magnetic fields.The response of these chambers has been shown to change, as a function of an external magnetic field [4][5][6][7][8][9].As such detectors are widely used for absolute dosimetric quality assurance, those changes have been taken into account by a dedicated correction factor, k B → ,Q , determined either using Monte-Carlo simulations or experimental setups [4][5][6][7][8][9][10].Because these correction factors cannot be determined in clinical routine, the extent to which generic, type-specific tabulated correction factors can be applied in dosimetry protocols is an important issue.Knowing the intra-type variation, quantifying chamber-to-chamber variations within the same chamber type, enables the user to assess the applicability and uncertainty of such correction factors.As conventional ionization chambers can lead to severe artefacts in MR-imaging, air-vented ionization chambers that produce fewer artefacts are needed for quality assurance of MR-based gating and tracking algorithms.
The MR-optimized ionization chambers studied in this paper were designed to meet these requirements.According to the vendor, the cavity dimensions, wall material, wall thickness and electrode is unchanged compared to the conventional types.In contrast to their conventional pendants, changes seem to be realized in the chamber stem to avoid artefacts in addition to production details to minimize air-layers in the chamber wall, which were observed in a recent study [9].Due to the design changes, it is unclear if correction factors for non-MR-optimized chambers are applicable.
Thus, the aim of this work was to experimentally investigate the magnetic field correction factor k B → ,Q along with its intra-type variation and its dependencies on magnetic flux density, energy and orientation for two MR-optimized chamber types, comparing them to their conventional counterparts.

Material and methods
Chamber readings were investigated for different magnetic flux densities B and beam qualities Q for four ionization chamber types: Semiflex3D-PTW31021 (SF), PinPoint3D-PTW31022 (PP), Semiflex3DMR-PTW31024 (SFMR), PinPoint3DMR-PTW31025 (PPMR) (PTW Freiburg, Germany).Measurements were carried out at Physikalisch-Technische Bundesanstalt (PTB, Germany) in a 6 x 20 x 20 cm 3 -water phantom using a mobile electromagnet (ER073W, Bruker, USA) placed in front of an Elekta Precise Linac (Elekta AB, Sweden), as specified previously [5].The source-to-surface distance (SSD) was 110 cm and the chamber axis was positioned perpendicular to the beam axis and magnetic field lines as shown in Fig. 1a.The reference point of the chambers was positioned at 10 cm water-equivalent depth.A photon beam was collimated to 4 x 10 cm 2 at the isocenter (SAD = 100 cm) by the MLCs.The magnetic flux density was assesed using a Hall sensor and a digital teslameter (DTM 151, Group3 Technology Limited, New Zealand).An in-house transmission monitor chamber [11] was used to monitor the accelerator's output and normalize the detector signals.
Each detector was pre-irradiated with at least 1000 MU.Measurement time was at least 80 s with constant dose rate.Each measurement signal was corrected for water temperature and atmospheric pressure.Given that only ratios of signals with and without magnetic fields are taken, polarity and recombination factors were not applied, since the literature indicates a neglectable or non-existent influence of the magnetic field on these factors [7].

Change of signal with change of magnetic flux density
To investigate the overall behavior of the signal of a certain chamber type in a magnetic field, the chamber reading was measured as a function of the magnetic flux density B at least once per chamber type using a nominal acceleration voltage of 6 MV.B ranged from − 1.5 to 1.5 T in steps of 0.2 T, with additional steps at ± 0.35 T.

Chamber reading correction factor
To investigate the magnetic field effect on the chamber reading, the correction factor k B → ,M,Q was assessed by the ratio of the chamber reading at a given beam quality without (M Q ) and with an external Magnetic flux densities representative of two MR-linacs (MRIdian, ViewRay, USA and Unity, Elekta AB, Sweden) were considered by carrying out five independent measurements for each of five chambers of each type in the 6 MV beam and magnetic flux densities of − 0.35 and − 1.5 T. The measurements were performed on five different days, including a full reposition of the chambers.A Mann-Whitney-U-Test was used to check for significant differences between the MR-optimized and the conventional chamber types.P-values < 0.05 were considered significant.

Consideration of different beam qualities
To derive k were determined for 6, 10 and 15 MV with magnetic flux densities of − 0.35 and − 1.5 T utilizing at least two chambers per chamber type.These measurements were repeated three times per chamber on different days.k B → ,M,Q was then expressed as a function of the beam quality specifier TPR 20,10 .This specifier is described in IAEA TRS-398 [12] and was 0.683, 0.733 and 0.760 for the three nominal accelerating voltages at the accelerator used in this work [13].A linear fit, and therefore c Q2Q1 for beam qualities of a 1.5 and a 0.35 T MR-linac.In this study we consider a nominal TPR 20,10 of 0.701 for the Unity MRlinac [10] and 0.648 for the MRIdian MR-linac [14].

Rotation of the chamber axis
In clinical routine, cylindrical ionization chambers are generally positioned antiparallel to the magnetic field.This was not possible in our experimental setup due to the limited space between the pole shoes of the electromagnet.A 1.5 T MR-linac was used to investigate the rotational dependency of the chamber response, using the quantity c rot as proposed by Pojtinger et al. [5].An MR-compatible water phantom (BeamscanMR, PTW) was used.Five independent measurements of the collected charge were performed, each done with a perpendicular (M B → ⊥ ,Q , Fig. 1a) and an antiparallel orientation (M B → ‖ ,Q , Fig. 1b) of the chamber axis with respect to the magnetic field for each of two individual chambers of the two MRoptimized ionization chamber types.The chambers were positioned with their reference point in the isocenter using MV imaging.The water depth was 10 cm and the SSD 133.5 cm.The gantry angle was set to 0 • and the photon beam was collimated to 10x10 cm 2 field size at the isocenter.For every measurement, the collected charge was measured ten times with an integration time of 10 s using an electrometer (Unidos Webline, PTW).The output of the Linac was monitored using an airvented ionization chamber (PTW31010, PTW) at a fixed position inside the radiation field.

Change in absorbed dose to water
To account for the change of the absorbed dose to water caused by an external magnetic field, a correction factor c B → can be applied [10].To determine c B → for the experimental setup at PTB, a complete accelerator head model of the Elekta Precise linac was simulated with the Monte Carlo system EGSnrc [15] (Version 2021) in BEAMnrc [16], and the dose to a water voxel was determined with the egs_chamber user code presented by Wulff et al. [17].
The c B → values for the 1.5 T MR-linac and a 0.35 T MR-linac, 0.9936 (20) and 0.9991(3), respectively, were taken from the literature [5,10]., which describes the magnetic field effects on the chamber response.

Magnetic field correction factork
Taking into account different beam qualities and chamber orientations by mean values of c Q2Q1 and c rot , k B → ,Q for perpendicular (Eq.5) and parallel (Eq.6) orientation can be calculated as follows:

Uncertainty
Uncertainties were calculated according to the Joint Committee for Guides in Metrology [18].A detailed description is given in the supplementary material B. It was assumed that all measurement results and calculated correction factors are normally distributed.Two uncertainties were calculated for each correction factor, k B → ,M,Q , cQ2Q1 , crot and k B → ,Q : ūind , representing the average uncertainty of all investigated individual chambers per chamber type, and ūgen , which additionally includes the intra-type variation as Type-B uncertainty.ūind can be compared to uncertainties in the literature, in which no intra-type variations were taken into account.ūgen should be used when the generic correction factors determined in this work are applied with an (arbitrary) chamber of this type for which no more detailed knowledge is available.

Change of signal with change of magnetic flux density
The change of signal with change of the magnetic flux density B for the investigated chambers is presented in Fig. 2. In general, an increasing |B| led to a decrease in chamber reading and an increase in intra-type variation.The ionization chamber types with a sensitive volume of 0.07 cm 3 , SF and SFMR, showed a similar behavior, while the two ionization chamber types with a sensitive volume of 0.016 cm 3 , PP and PPMR, differed more strongly.

Chamber reading correction factor
was investigated in more detail for the magnetic flux densities of -0.35 and − 1.5 T. The results are presented in Fig. 3 and Table 1.For each chamber type, the mean standard deviation, SD(k ), of reproducibility were about twice as large at -1.5 T as they were at -0.35 T. The intra-type variation, represented by ) , was more than three times as large (Table 1).
In case of B = -0.35T, significant differences were found between SFMR and SF chambers (p = 0.01), while no significant differences were found between PPMR and PP chambers (p = 0.15).For B = -1.5 T, significant differences between PPMR and PP chambers were observed (p = 0.03), whereas no significant differences were seen between SFMR and SF (p = 0.42).S1).The correction factors cQ2Q1 for the transition between PTB and MR-linac beam qualities are presented in Tables 2 and 3.

Rotation of the chamber axis
Supplementary Figure S2 shows the effect of rotating the chamber axis with respect to the magnetic field of a 1.5 T MR-linac from a perpendicular to an antiparallel orientation.Both chamber types showed an increase in chamber response.In case of the SFMR, the mean increase of the response was 6.1%, resulting inc rot = 0.9427 with a standard deviation of 0.0027.For the PPMR, the mean increase of the chamber response was 4.1%, making crot equal to 0.9603 with a standard deviation of 0.0018.   2 and 3.

Discussion
In this work, the characteristics of two novel MR-optimized ionization chambers, SFMR and PPMR, and their conventional counterparts, SF and PP, were investigated regarding their behavior inside an external magnetic field.Magnetic field correction factors k B → ,Q were derived for multiple beam qualities, magnetic flux densities B and chamber axis orientations.The use of several chambers of the same type further allowed the assessment of the intra-type variation.
The signals as a function of B determined in this work for chambers of types SF and PP were in good agreement with previously reported data by Delfs et al. and Cervantes et al. [9,19].The design changes made to the MR-optimized chambers had a greater impact on the PPMR type chambers than the SFMR type chambers.
With increasing |B|, the range of reproducibility and the intra-type variation of k B → ,M,Q increased.A similar method and the same experimental setup were employed by Pojtinger et al. [5] to examine two of the SF chambers (S/N141576 / S/N141577) also used in this work.There, , given B = -1.5 T, was found to differ by 0.7% between the two chambers (1.0481/1.0549).We were able to reproduce these results (1.0477/1.0545).Moreover, by using five chambers of this type, we found that one chamber (S/N141577) differed from the mean of the four other chambers, demonstrating a high intra-type variation.
In the case of the PPMR type chambers, one individual chamber exhibited a behaviour different from the other four chambers.With B = -1.5 T, of chamber S/N200589 differed from the mean of the other chambers by 1.2%.All geometric chamber parameters were within the manufacturers tolerances according to a X-ray examination and consultation with the manufacturer.Air gaps at the chamber wall, as indicated by Cervantes et al. [9] were not observed.Also, no correlation between the calibration factor and k B → ,M,Q was found.
c Q2Q1 was very uniform per chamber type and over all chamber types.Even in case of chamber SF-141577, where in the presence of a 1.5 T magnetic field differed by about 0.7% from the mean of the other chambers, c Q2Q1 deviated by less than 0.1% from the mean cQ2Q1 of this chamber type.c Q2Q1 was not reported in detail by Pojtinger  (5).The first uncertainty is ūind , which represents the average uncertainty of x j for a single chamber, the second uncertainty is ūgen , which represents the uncertainty of x j for an arbitrary chamber using the general correction factor determined in this work and therefore includes intra-type variation.Data with * was taken from [10].4), (5) and (6).The first uncertainty is ūind , which represents the average uncertainty of x j for a single chamber, the second uncertainty is ūgen , which represents the uncertainty of x j for an arbitrary chamber using the general correction factor determined in this work and therefore includes intra-type variation.Data with * was calculated/taken from [5].

B→
,M,Q for any other beam quality than the one used in this work, we propose the quantity c Q2Q1 .It is the ratio of k B → ,M,Q at the desired beam quality Q 2 and the beam quality Q 1 for which k B → ,M,Q was originally determined.

Fig. 1 .
Fig. 1. Chamber setups used in this study: a) chamber axis perpendicular to the magnetic field B → and irradiation beam axis γ → .With positive B-values, the initial Lorentz force F → L for electrons moving along the beam axis points to the chamber stem.Negative B-values result in the Lorentz force pointing to the chamber tip.b) chamber axis antiparallel to the magnetic field and perpendicular to the beam axis.

B
Two mean values per chamber type were defined for the evaluation of the correction factorsk B → ,M,Q , c Q2Q1 , c rot and k B → ,Q: the arithmetic mean of a correction factor x i,j of repeated measurements i for a single chamber j, named xj , and the arithmetic mean of xj for all individual chambers j, x.The mathematical definition of xj , x, together with the definition of their respective standard deviation SD(x) and range R(x) can be found in the supplementary material A. As presented by van Asselen et al.[10], the change in chamber reading and change in absorbed dose to water can be used to derive k B → ,Q

Figure
Figure S1 in the supplementary material C shows the energy dependence of k B → M,Q for 6, 10 and 15 MV for magnetic flux densities of − 0.35 and − 1.5 T. All linear regressions resulted in coefficients of determination of R 2 > 0.99 (TableS1).The correction factors cQ2Q1 for the transition between PTB and MR-linac beam qualities are presented in Tables2 and 3.

3. 5 .
Change in absorbed dose to water The Monte Carlo simulation of the 6 MV PTB-setup yielded c B → values of 0.9992(25) and 0.9967(25), corresponding to magnetic flux densities of 0.35 and 1.5 T, respectively.

Fig. 2 .
Fig. 2. Normalized signal as a function of magnetic flux density B of four chamber types, two with a sensitive volume of 0.07 ccm (SF and SFMR, left) and two with a sensitive volume of 0.016 cm 3 (PP and PPMR, right).The MR-optimized chambers were only measured once per chamber type.For the mean values of the conventional chamber types, the range band shows the maximum and minimum values of the five individual chambers.

Fig. 3 .
Fig. 3. k B → ,M,Q for B = -0.35T (first column) and B = -1.5 T (second column) as measured at a 6 MV beam on five different days, including a full reposition for five chambers of four chamber types.The MR-optimized chambers (SFMR/PPMR) are compared to their conventional counterparts (SF/PP).The horizontal line marks the mean value per individual chamber, the interval depicts the standard deviation.

Table 1
Mean, standard deviation and range of k represent the mean standard deviation and range over individual chambers.As such they provide information on the reproducibility of the measurements.) represent the standard deviation and range of all chambers of one chamber type and thus provide information about the intratype variation.The definitions of these quantities can be found in supplementary material A.

Table 2
Summary of results: mean and standard uncertainties of different quantities x i for B = -0.35T and Q = 0.683(PTB)/0.648(0.35T MR-linac).

Table 3
Summary of results: mean and standard uncertainties of different quantities x i for B = -1.5 T and Q = 0.683 (PTB)/0.701(1.5 T MR-linac).The values of k B → ,M,Q , cQ2Q1 and crot represent the means of these factors measured with different chambers of the same type.These mean values were used to calculate k B → ,Q using equations (